REPUBLIC OF TRINIDAD & TOBAGO MINISTRY OF EDUCATION
ASSESSMENT FRAMEWORK FOR THE SECONDARY ENTRANCE ASSESSMENT 2019-2023
Subjects Scores & No. of Items
Objectives
Purpose
Item formats
Timing
Types of Thinking
Ministry of Education Education Tower, #5 St Vincent Street, Port of Spain September 2017
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TABLE OF CONTENTS
Foreword……………………………………………………… Foreword………………………… …………………………………………………. …………………….
3
Components of Secondary Entrance Assessment 2019 – 2023…………... – 2023…………..................
4
Weight of Papers and Placement in Secondary Schools…………………………….
6
English Language Arts (ELA) Writing Paper……………………………………….
7
English Language Arts Paper- Spelling, Punctuation, Punctuatio n, Capitalisation, Grammar and Reading Comprehension…………………………………………………………….
8
Assessment Objectives for the English Language Arts Paper: Reading Comprehension………………………………………………………………………
10
Reading Comprehension Thinking Processes…………………….… Processes…………………….………… ………
10
Objectives and Processes for Non-fiction Non-fiction Text (Content area)…..................
12
Objectives and Processes for Literary Texts (Poems and Stories)..................
12
Objectives and Processes for Graphic Texts………………………………...
13
Grammar in Context…………………………………...…………………….
13
Spelling and Vocabulary……………………………………………………
14
Capitalisation and Punctuation……………………...……………………....
15
Mathematics Paper ……………………...……………………...…………………… ……………………...……………………...……………………
16
Mathematical Thinking Processes………………………………………….
17
Distribution of Marks by Strands and Thinking Processes…………………
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Assessment Objectives for the Mathematics Paper ……………………........ ……………………........
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Objectives and Thinking Processes for Number …………………….... …………………….............
20
Objectives and Thinking Processes for Measurement ………………............
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Objectives and Thinking Processes for Geometry…………………………..
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Objectives and Thinking Processes for Statistics……………………............
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Foreword
The Assessment Framework for the Secondary Entrance Assessment (SEA) 2019-2023 specify the purpose, components, format and content of the SEA. The Assessment is based on the English Language Arts and Mathematics Curriculum Guides (2013). The specific English Language Arts skills to be assessed are English Language Arts Writing, Spelling, Grammar, Punctuation,
Capitalisation
and
Reading
Comprehension.
In
Mathematics,
Number,
Measurement, Geometry and Statistics are assessed. The Secondary Entrance Assessment facilitates the transition from primary to secondary school. The Assessment Framework for SEA 2019 - 2023 is intended to assist teachers and all those involved in the preparation of students for secondary school. It is anticipated that the specifications for each paper will allow teachers to better assist students in understanding the format and requirements of the Secondary Entrance Assessment. It is hoped that through use of a student-centred approach to teaching, with a focus on the development of a range of skills at different levels of thinking, our students will be better prepared for the opportunities available at the secondary level and life in general. There are changes that teachers and other stakeholders are asked to note. These include the: ▪
reduction in the number of items in the Mathematics and English Language Arts papers
▪
introduction of explicit levels of thinking for the objectives that are assessed for Reading Comprehension and Mathematics
▪
assessment of spelling, punctuation, capitalisation and grammar in context (short passages)
▪
incorporation of money as a component under the number strand in Mathematics
▪
use of prose/fictional passages as part of the comprehension
▪
increased emphasis on Reading Comprehension
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Components of Secondary Entrance Assessment 2019-2023
The Ministry of Education is pleased to present to teachers, the Assessment Framework for the Secondary Entrance Assessment (SEA) 2019-2023. The SEA is a public examination that facilitates placement of students in secondary schools in Trinidad and Tobago based on the following criteria: ▪
Parents’ choices
▪
Students’ performance by order of merit
▪
Principals’ 20% selection (Denominational schools)
▪
Gender
▪
Residence
▪
Multiple births
The Secondary Entrance Assessment comprises three papers that all candidates must attempt: 1. English Language Arts Writing 2. Mathematics 3. English Language Arts (Spelling, Punctuation, Capitalisation, Grammar, and R eading Comprehension)
The duration of each paper is indicated in Table 1. Table 1: Duration of SEA Papers
Paper
Time Allotment
English Language Arts Writing
Fifty (50) minutes
Mathematics
Seventy-five (75) minutes
English Language Arts
Seventy-five (75) minutes
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The schedule of the working time, the total time for the administration of the assessment and the number of items in each test are shown in Table 2. The total time for the administration of the assessment is approximately 4 hours 30 minutes while the actual working time for the candidates is 3 hours 20 minutes.
Table 2: Working Time, Total Administration Time and Number of Items for the SEA Papers
Activity
Time (Minutes) Distribution of Booklets
Completion of the English Language Arts Writing Test Completion of the Mathematics Test
Reading of Directions
Number of Items
Working Time
Collection of Booklets
Total Time
5
3
50
5
63
1
5
3
75
5
88
45
B R E A K
Completion of the English Language Arts Test TOTAL
3 0
5
3
75
5
88
43
15
9
200
15
239
89
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Weighting of Papers and Placement in Secondary Schools
The weighting of the Mathematics, English Language Arts and ELA Writing papers is 100:60:40. Students’ scores in each paper will be converted to standard scores and weighted as shown in Table 3. The weighted scores will then be combined and the combined score (composite score) used for placement of students in secondary schools. Standard scores utilise the variance in each paper and therefore allow the student’s relative standing (position) in each paper to be maintained when they are combined, thus ensuring fairness in the placement process.
Table 3: Weighting of SEA Papers
Paper
Weighting
Mathematics
100
English Language Arts
60
English Language Arts Writing
40
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English Language Arts (ELA) Writing Paper
The English Language Arts Writing paper will contain three items randomly assigned in any one year: Either
(i) Three (3) narrative items
Or
(ii) Three (3) expository items
Students will be asked to respond to one item which will be scored by two persons. Each response will be scored based on the following criteria: ▪
Content
▪
Language Use
▪
Grammar and Mechanics
▪
Organisation
General Assessment Objectives for ELA Writing Students will: Demonstrate knowledge of narrative and expository writing Write stories and simple reports (expository) Use descriptive language and sensory details appropriate to stories Use figurative language appropriate to stories Use factual details appropriate to reports Use formal language and tone appropriate to reports Express written ideas clearly and coherently Generate a variety of sentence types Demonstrate accurate use of grammar, spelling and mechanics Demonstrate effective organisation of ideas
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ELA - Spelling, Punctuation, Capitalisation, Grammar, and Reading Comprehension
The English Language Arts assessment will comprise Spelling, Punctuatio n, Capitalisation Grammar, and Reading Comprehension. The assessment objectives are taken from Standards Three, Four and Five as specified in the National Primary School Curriculum (2013). This is built on the understanding that many of the foundation skills developed during Infant and Junior school act as building blocks. The English Language Arts paper is designed to assess spelling, punctuation, capitalisation and grammar in context. This means that discrete sentences will be replaced by short continuous text to which students will be required to respond. The reading comprehension section will assess different levels of thinking. Passages will be complemented by simple visuals designed to reflect authentic reading material. Additionally, prose material, introduced for the first time, will be alternated with the other type of texts. Vocabulary will be assessed in context; that is, in the Reading Comprehension component of Section II. Table 4 displays the changes to the English
Language Arts format for SEA 2019 - 2023 in comparison with SEA 2016. Table 4: Comparison of SEA 2016 and SEA 2019 - 2023 Components of SEA 2016
Components of SEA 2019 - 2023
Section 1: Grammar Skills: (22 items) - Nouns: 4 items Part of Speech: 3 items Verbs: 3 items Direct speech: 2 items Active voice: 2 items Correct form of words: 3 items Conjunctions: 2 items Grammatical error: 3 items Section II: Vocabulary: 6 items Spelling: 3 items Punctuation: 4 items Section III: Non-fiction text: 5 items; (includes two parts (a) and (b) Fiction (poetry): 5 items; (includes two parts (a) and (b) Graphic: 5 items (includes two parts (a) and (b)
Section 1: Spelling: 6 items Punctuation and Capitalisation: 6 items Grammar Skills: 6 items
•
• • •
•
•
•
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▪ ▪ ▪
Section II: Non-fiction text or Fiction text: 10 items Poetry: 10 items Graphic Text: 5 items ▪ ▪ ▪
The English Language Arts Paper consists of forty-three (43) items and assesses the following language skills from the Republic of Trinidad and Tobago Primary School Curriculum - English Language Arts (2013). ▪
Spelling
▪
Punctuation and Capitalisation
▪
Standard English Grammar
▪
Reading Comprehension
Extract of non-fiction text or fiction text
Poetry
Graphic text
The English Language Arts Paper will be scored out of a total of eighty (80) marks (Table 5). Items in Section I (Spelling, Punctuation, Capitalisation, and Grammar) will be worth thirty (30) marks, while items in Section II (Reading Comprehension) will be worth fifty (50) marks.
Table 5: Distribution of English Language Arts Items (Section I) Language Focus Revision of spelling within context
No. of Items 6
No. of Marks 12
Revision of punctuation and capitalisation within context
6
6
Revision of grammar within context
6
12
No. of Items 10
No. of Marks 20
Poetry
10
20
Graphic text
5
10
TOTAL
43
80
(Section II) Reading Comprehension Non-fiction text or fiction text
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Assessment Objectives for the English Language Arts Paper: Comprehen sion
The SEA English Language Arts assessment objectives are embedded in the Republic of Trinidad and Tobago Primary School Curriculum - English Language Arts (2013). Educators are directed to the English Language Arts programmes for Standards Three, Four and Five. Based on the comprehension purposes and levels, the SEA will assess students’ ability to understand the following: ▪
Non-fiction text or fiction text
▪
Poetry
▪
Graphic text
It should be noted that “all texts are not equal and can vary with regard to length, syntactic complexity, abstractness of ideas, and organizational structure” (Mullis, Martin, Sainsbury, 2016,
p. 18). However, all passages will be selected based on the appropriate readability levels. Reading Comprehension Thinking Processes
The SEA will assess three types of reading comprehension thinking processes within each of the three texts, these are: ▪
Literal
▪
Inferential
▪
Evaluation and appreciation
Table 6 displays the Reading Comprehension Processes and percent associated with each type of text. The Processes are more specific to comprehension, unlike Bloom’s Taxonomy which was used in the previous SEA Guidelines. Table 6: Reading Comprehension Processes by Text Type Text Type
Reading Comprehension Processes Literal 30%
Inferential 40%
Evaluation/Appreciation 30%
2. Poetry
30%
40%
30%
3. Graphic
40%
40%
20%
1. Non-fiction or Fiction
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Literal
This involves giving attention to information explicitly stated by the author. In this process, readers seek to understand the straightforward meaning of the text, such as facts, vocabulary, dates, times and locations (Day & Park, 2005). Such questions can be answered directly and explicitly from the text. A more complex task might be the recognition or recall or a series of facts or the sequencing of incidents in a reading selection. For example: Where did the story take place?
Inferential
Making inferences involves more than just a literal understanding. Students may initially have difficulty with responses to these questions because the answers are in the text but are not explicitly stated (Day & Park, 2005) and thus the connections need to be inferred (Mullis, Martin & Sainsbury (2016). Skilled readers are often able to make these connections automatically (West & Stanovich, 2000). According to Mullis, Martin & Sainsbury (2016), “With this type of processing, readers typically focus on more than just word, phrase, or sentence-level meaning. While the focus may be on local meaning residing within one part of the text, the focus also may be on more global meaning, representing the whole text” (p.20). For example: What might have happened if Rapunzel did not have long hair?
Evaluation/Appreciation
As readers evaluate the content of the text, the focus shifts from constructing meaning to critically considering the text itself (Mullis, Martin & Sainsbury, 2016). In terms of appreciation, readers connect emotionally and aesthetically with the text. It is an emotional response to the literary techniques, forms, styles, and structures. While no such responses are incorrect, they cannot be unfounded; they must relate to the content of the text and reflect a literal understanding of the material (Day & Park, 2005). For example, “What do you like or dislike about this passage? Students will have to use both their literal understanding and th eir own ”
knowledge to respond.
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Objectives and Reading Comprehension Processes for Non-fiction Text (Content Area) Objectives
Processes
1.
Identify main idea from text
Literal
2.
Identify supporting details from text
Literal
3.
Literal
6.
Determine the contextual meaning of words and phrases in factual texts Demonstrate an understanding of supporting details and show their relationship within text Use pictures, words, definitions and context clues to infer meanings in context Analyse simple details and represent in graphic organisers
7.
Explain cause and effect relationships in texts
Inferential
4. 5.
Inferential Inferential Inferential
8.
Evaluate texts by making explicit and inferential reference to Evaluation and Appreciation texts 9. Identify the connotative meanings of familiar and new words Inferential contextually 10. Express preferences and support their views by reference to texts Evaluation and Appreciation 11. Support personal views with reference to text
Evaluation and Appreciation
12. Understand that texts have purposes and are written for audiences.
Evaluation and Appreciation
Objectives and Reading Comprehension Processes for Literary Texts (Poems and Stories) Objectives 13. Retrieve information that is stated explicitly
Processes Literal
14. Use context-clues (word structure clues, definition clues) and background knowledge to determine the meaning of words or phrases 15. Explore the mood of a literary piece
Inferential
16. Identify words/language used to create specific moods
Inferential
17. Identify words/language used to appeal to the senses
Literal
18. Identify figures of speech in literary texts (simile, metaphor, personification)
Literal
19. Identify imagery in literary texts
Inferential
20. Examine the writer’s and the reader’s points-of-view
Evaluation and appreciation
21. Draw conclusions (about characters, setting and events) based on evidence provided in literary text.
Inferential
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Evaluation and appreciation
Objectives 22. Infer meaning (cause and effect) as they relate to literary texts
Processes Inferential
23. Offer solutions to major conflicts in the text
Evaluation and Appreciation
24. Identify tone in poems and prose
Inferential
25. Make judgements on the behaviour of characters
Evaluation and Appreciation
26. Judge the nature of characters with supporting evidence
Evaluation and Appreciation
27. Make connections between literature and real-life situations
Inferential
Objectives and Reading Comprehension Processes for Graphic Texts Objectives 28. Comprehend content (message, in print text and visual media.)
Processes Inferential
29. Explain the purpose of selected media texts
Inferential
30. Identify implied messages in selected media texts based on elements of design 31. Identify overt messages in selected media texts based on elements of design 32. Recognize that different media forms use particular language styles and techniques in their construction 33. Analyse selected media to understand how information/ messages are presented to audiences 34. Evaluate techniques used in media texts
Inferential Literal Inferential Evaluation and appreciation Evaluation and appreciation
Grammar in context
1.
Use parts of speech with correct verb tense and concord in writing
2.
Ensure noun and pronoun concord
3.
Ensure agreement of subject and verb and subject and pronoun
4.
Use Nouns: common, proper, collective and abstract in sentences
5.
Use Adjectives: comparative and superlative degree
6.
Use Pronouns: Personal, Possessive, Reflexive and Relative Pronoun.
7.
Use Adverbs: comparative and superlative forms
8.
Use Prepositions in context
9.
Use Conjunctions to combine ideas and sentences
10.
Use nouns, subject pronouns, verbs, adjectives and conjunctions to form compound sentences 13
11.
Use a conjunction to join a main clause and subordinate clause to form a complex sentence
12.
Use verbal forms: simple present, past, future, present continuous tense, past perfect tense
13.
Use the correct form of the verb in writing
14.
Use regular and irregular verb forms
15.
Choose verbs to agree with subjects in number
16.
Ensure concord in sentences that contain parenthetical phrases
17.
Use modals: can, may, should, would, could, might
18.
Use participles-past and present
19.
Use adverbs: comparative and superlative forms
20.
Make new words by adding prefixes and suffixes to root words
21.
Use prepositions in context.
22.
Recognize the function of prepositions, adverbs, adjectives, nouns, verbal forms and conjunctions in context
23.
Revise concord, choice of vocabulary and spelling in own sentences
Spelling and Vocabulary
1.
Apply spelling rules when writing. Produce the following correctly: - plural forms in which ‘y is changed to ‘i’ and ‘f’ to ‘v’ before adding an “es” ending - words that double the final consonant before adding endings - word s that drop the final ‘e’ before an ending - ‘ie’ and ‘ei’ words - words with hard and soft ‘c’ and ‘g’ - words with silent letters - common homophones
2.
Use spelling rules in writing. Produce the following correctly: - convert compound words into plural forms - when a word ends in a silent ‘-e’, drop the ‘-e’ before adding -ing - for action words that end in ‘ -ie’, change the ‘-ie’ to a ‘-y’ before adding ‘ing’ - when the suffix -full is added to the end of a base word, drop one ‘-l’
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-
double the last letter of words ending in a short vowel followed by a single consonant before adding a ‘-y’ e.g. bag - baggy
-
add a ‘-y’ to words ending with two consonants to form describing words e.g. dirt-
dirty -
for words ending in a silent ‘ -e’, drop the ‘-e’ before adding ‘-y’ e.g. ice-icy
3.
Make new words by adding prefixes and suffixes to root words
4.
Use the different types of vocabulary in context across content areas: technical terms; synonyms; antonyms; homophones; homographs; words with multiple-meanings
5.
Discover and correct misspelt words
Capitalisation and Punctuation
1.
Use punctuation marks and capital letters correctly in writing
2.
Use the colon and quotation marks for dialogue, titles and direct speech
3.
Use the following punctuation marks in sentences: full stop, question mark, exclamation mark, apostrophe in contractions and possessives, quotation marks, colons and commas
4.
Use capital letters in sentences for: first word in a quotation; title of books, chap ters, poems; title of proper names; important words in headlines, subject heading
5.
Edit capitalisation and punctuation in sentences
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Mathematics Paper
The Mathematics paper consists of 45 items and encompasses the four strands of the syllabus. •
Number
•
Measurement
•
Geometry
•
Statistics
Money has now been incorporated into the number strand. The SEA will assess three types of thinking processes within each of the four strands. These processes – knowing, applying and reasoning – have incorporated those currently used in the Republic of Trinidad and Tobago Primary School Curriculum- Mathematics (2013) and are in conformity with international best practices (Grønmo, Lindquist, Arora, & Mullis, 2015). Distribution of Marks by Section
The paper is divided into three sections as displayed in Table 7. Details in terms of the allocation of marks and items by strands and sections are identified at Tables 8a and 8b, respectively. Sections I and II remain unchanged in terms of the number of items and the score for each. However, Section III comprises 5 items each worth 4 marks, instead of 6 items each worth 5 marks as detailed in the previous Secondary Entrance Assessment Guidelines. Table 7: Distribution of Mathematics Items and Marks by Section Section
No. of Items
Marks per Item
Section I
20
1
Section II
20
2 or 3
Section III
5
4
16
Table 8a: Distribution of Marks by Strands and Sections Strands
Section I
Section II
Section III
Total Marks
Number
10
25
8
43
Measurement
4
10
4
18
Geometry
3
7
4
14
Statistics
3
8
4
15
Total
20
50
20
90
Table 8b: Distribution of Items by Strands and Sections Strands
Section I
Section II
Section III
No. of Items
Number
10
10
2
22
Measurement
4
4
1
9
Geometry
3
3
1
7
Statistics
3
3
1
7
Total
20
20
5
45
Mathematical Thinking Processes
The SEA will assess three types of mathematical thinking processes within each of the four strands, these are: ▪
Knowing
▪
Applying
▪
Reasoning
Table 9 displays the thinking processes and percentages associated with each strand. Such processes are designed to indicate what students are able to do with the content.
The
Mathematical Thinking Processes are more specific to Mathematics and reflect a more contemporary approach unlike that which was used in the previous SEA Guidelines.
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Distribution of Marks by Strands and Thinking Processes Table 9: Number of Items by Thinking Processes Strands
No. of Items
Knowing
Applying
Reasoning
Number
22
40%
40%
20%
Measurement
9
40%
40%
20%
Geometry
7
40%
40%
20%
Statistics
7
40%
40%
20%
Knowing
The ability to use or apply mathematical reasoning and problem solving is premised on the understanding that the student has a level of familiarity with mathematical concepts and fluency in mathematical skills (Grønmo, Lindquist, Arora, & Mullis, 2015). Grønmo et al. (2015) further assert that knowing enables “easy recall of the language and basic facts and conventions of number, symbolic representation, and spatial relations”. There are several aspects of knowing,
including recall, recognize, classify/order, compute, retrieve and measure.
Recall Recognize
Classify/Order Compute Retrieve Measure
Recall definitions, terminology, number properties, units of measurement, geometric properties, and notation. Recognise numbers, expressions, quantities, and shapes. Recognise entities that are mathematically equivalent (e.g., equivalent familiar fractions, decimals, and percents; different orientations of simple geometric figures). Classify numbers, expressions, quantities, and shapes by common properties. Carry out algorithmic procedures for +, – , ×, ÷, or a combination of these with whole numbers, fractions, and decimals. Retrieve information from graphs, tables, texts, or other sources. Use measuring instruments; and choose appropriate units of measurement.
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Applying
The applying domain involves the application of mathematics in a range of contexts (Grønmo, et al., 2015). In some items aligned with this domain, students need to apply mathematical knowledge of facts, skills, and procedures or understanding of mathematical concepts to create representations. Representation of ideas form the core of mathematical thinking and communication, and the ability to create equivalent representations is fundamental to success in the subject. Problem solving is central to the applying domain, with an emphasis on more familiar and routine tasks. Problems may be set in real-life situations, or may be concerned with purely mathematical questions involving, for example, numeric expressions, geometric figures, or statistical data sets. Various aspects of applying are further explained below.
Determine Represent/Model
Implement
Determine efficient/appropriate operations, strategies, and tools for solving problems for which there are commonly used methods of solution. Display data in tables or graphs; geometric figures, or diagrams that model problem situations; and generate equivalent representations for a given mathematical entity or relationship. Implement strategies and operations to solve problems involving familiar mathematical concepts and procedures.
Reasoning
Reasoning mathematically involves logical, systematic thinking (Grønmo, et al. 2015). It includes intuitive and inductive reasoning based on patterns and regularities that can be used to arrive at solutions to problems set in novel or unfamiliar situations. Such problems may be purely mathematical or may have real-life settings. Both types of items involve transferring knowledge and skills to new situations; and interactions among reasoning skills usually are a feature of such items. Reasoning involves the ability to observe and make conjectures. It also involves making logical deductions based on specific assumptions and rules, and justifying results. Various aspects of reasoning are highlighted below.
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Analyse Integrate/Synthesize Evaluate Draw Conclusions Generalize Justify
Determine, describe, or use relationships among numbers, expressions, quantities, and shapes. Link different elements of knowledge, related representations, and procedures to solve problems. Evaluate alternative problem-solving strategies and solutions. Make valid inferences on the basis of information and evidence. Make statements that represent relationships in more general and more widely applicable terms. Provide mathematical arguments to support a strategy or solution.
Assessment Objectives for the Mathematics Paper
Objectives and Thinking Processes for Number Strand Objectives
Processes
Whole Numbers
1. Represent any number up to one million using numerals or word names.
Knowing
2. Represent whole numbers to 1000 000 using multiple models and connect to numerals and number names. 3. Represent a number up to 1 million concretely, pictorially, symbolically.
Knowing
4. State the value or place value of a digit in any whole number up to one million. 5. Express a whole number up to one million using expanded notation.
Knowing
6. Write the numeral represented by a given expanded notation .
Knowing
7. Order whole numbers to one million.
Knowing
8. Compare whole numbers to one million
Knowing
9. Round whole numbers to the nearest thousand.
Knowing
10. Solve problems in addition (sum less than 10 000) and subtraction (minuend less than 10 000) 11. Multiply two, three and four digit numbers by one or two-digit multipliers.
Applying
12. Divide two, three and four digit numbers b y one or two digit divisors with and without remainder.
Knowing
13. Use estimation strategies in problem solving contexts with whole numbers.
Reasoning
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Applying
Knowing
Knowing
Objectives
Processes
14. Use estimation skills to check solutions to problems and determine reasonableness of answer. 15. Solve one-step word problems involving any one of the four basic operations on whole numbers. 16. Solve multi-step words problems involving any combination of the four basic operations on whole numbers. 17. Explain or demonstrate how an answer was obtained when solving problems. 18. Calculate the square of a number
Reasoning
19. Differentiate between factors and multiples and prime and composite numbers and identify square numbers. 20. Calculate the square root of a perfect square.
Applying
21. List square numbers up to 144.
Knowing
22. Explore patterns involving square numbers up to 144 and square roots up to 12. 23. Explore patterns involving square roots up to 12.
Reasoning
24. Solve problems involving the use of number patterns. 25. Explore repeating, increasing and decreasing patterns. 26. Calculate the unknown in number sentences involving the four operations and explain procedures used. 27. Interpret the remainder in relation to the context of word problems.
Reasoning Reasoning Applying
28. Explain why a remainder is obtained for some division problems.
Reasoning
29. Identify the missing numbers in an ordered sequence or on a number line.
Reasoning
30. Use a pattern rule to determine missing elements for a given pattern and to extend or predict subsequent elements in patterns. Fractions
Reasoning
31. Represent a fraction using pictorial and symbolic representations.
Applying
32. Generate equivalent fractions using a variety of models.
Applying
33. Order proper fractions with unlike denominators using equivalent forms.
Reasoning
34. Demonstrate an understanding of proper fractions, improper fractions and mixed numbers.
Reasoning
35. Express improper fractions as mixed numbers.
Knowing
36. Express mixed numbers as improper fractions.
Knowing
37. Add and subtract fractions involving same denominator.
Knowing
38. Add and subtract fractions involving one denominator as a multiple of the other. 39. Subtract a fraction from a whole number.
Knowing
40. Add a fraction to a whole number.
Applying 21
Applying Reasoning Reasoning Knowing
Knowing
Reasoning
Reasoning
Applying
Objectives
Processes
41. Subtract two fractions (including whole/mixed numbers).
Applying
42. Calculate fractions of a collection or set.
Knowing
43. Express one quantity as a fraction of another.
Knowing
44. Calculate the whole given a part as a unit fraction.
Knowing
45. Solve problems involving the multiplication of a fraction b y a whole number. 46. Solve problems involving the multiplication of a fraction by a fraction
Applying
47. Solve problems involving the multiplication of a fraction by mixed numbers. 48. Divide a whole number by a fraction.
Applying
49. Divide a fraction by a whole number.
Applying
50. Divide a fraction by a fraction.
Applying
51. Multiply fractions by whole numbers.
Applying
52. Solve one-step problems involving fractions.
Applying
53. Solve multi-step problems involving fractions.
Reasoning
54. Solve real-life problems involving fractions and using the algorithms developed. Decimals
Reasoning
55. State the place value of digits in decimal fractions up to hundredths. 56. Explore the place value of decimals to hundredths including expanded notation. 57. State the value of digits in decimal fractions up to hundredths. 58. Compare and order decimals up to hundredths. 59. Express decimal fractions using expanded notation.
Knowing Applying
60. Convert expanded notation to decimal fractions.
Knowing
61. Arrange decimal fractions in ascending and descending order (up to hundredths). 62. Round decimals to the nearest whole number and tenths.
Knowing
63. Solve problems involving the addition and subtraction of decimals including money.
Reasoning
64. Solve problems involving the multiplication of a decimal b y a whole number. 65. Solve problems involving the multiplication of tenths by tenths.
Applying
Applying
Applying
Knowing Applying Knowing
Knowing
Applying
66. Relate decimals to fractions and money. 67. Solve problems involving the division of a decimal fraction by a whole number (dividend up to 2 decimal places).
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Reasoning
Objectives
Processes
68. Use a number of strategies to solve routine and non-routine problems involving decimals. 69. Express decimals as common fractions. 70. Use decimal notation as another form of writing base ten fractions (tenths, hundredths). 71. Solve real-world problems involving the addition and subtraction of decimals to hundredths using the algorithm. Percent
Reasoning
72. Calculate simple percent of quantities e.g.10% of $200 = 1/10 of $200 = $20. 73. Express percentages (e.g. 50%, 25%, 20% and 10%) as fractions (e.g. ½, ¼, 1/5, 1/10). 74. Express percentages (e.g. 50%, 25%, 20% and 10%) as decimals (e.g. 0·5, 0·25, 0·2 and 0·1). 75. Order fractions, decimals and percentages. 76. Express quantities as percentages of other quantities.
Knowing
77. Solve one – step problems involving percentages (no gain and loss per cent, no calculation of whole quantities given parts expressed as percent and no calculations of part of quantities given another part expressed as a per cent). 78. Solve multi – step problems involving percentages (no gain and loss percent, no calculation of whole quantities given parts expressed as per cent and no calculations of part of quantities given another part expressed as a per cent). 79. Identify coins, bills, their value and the value of a set of coins/bills (up to 100 cents and $100). 80. Determine the possible combinations of coins/bills, which are equal to given amounts (up to 100 cents and $100).
Applying
81. Record money values using decimals.
Knowing
82. Calculate total cost and the change in money transactions.
Applying
83. Solve real-life, one-step problems involving whole numbers, (including profit and loss, best buy, discount, savings, salaries, wages, loans, simple interest, VAT). 84. Solve real-life, multi-step problems involving whole numbers, (including profit and loss, best buy, discount, savings, salaries, wages, loans, simple interest, VAT). 85. Solve problems involving direct proportions.
Applying
86. Solve problems involving unequal sharing (not including the use of ratio).
Reasoning
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Knowing Knowing Applying Applying
Reasoning
Knowing Reasoning
Reasoning
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Objectives and Thinking Processes for Measurement Strand Processes
Objective Linear Measure
87. Select and use the most appropriate standard unit for measuring various lengths/distances. 88. Convert linear measure from one form to the other (millimetres, centimetres, metres, kilometres).
Knowing
89. Apply decimal knowledge to record measurements. e.g. 123cm = 1.23m
Applying
90. Solve computational problems involving the metre and the centimetre by using the relationship between them. 91. Write and explain the formulae for finding the perimeter of any given rectangle and square.
Reasoning
92. Calculate and compare perimeters of squares and rectangles.
Applying
93. Construct or draw two or more rectangles for a given perimeter in a problemsolving context. 94. Find the perimeters of simple composite figures that may be dissected into rectangles and squares. 95. Solve problems in real-life contexts involving perimeter.
Reasoning
96. Solve problems involving length.
Reasoning
97. Solve problems involving perimeter of compound shapes.
Reasoning
Knowing
Reasoning
Applying Reasoning
Area
98. Select the appropriate unit of measure when measuring surfaces of varying sizes and explain the suitability of the unit. 99. Write and explain the formula for finding the area of squares and rectangles.
Knowing
100. Compare and order area of surfaces and explain reasoning using appropriate vocabulary. 101. Approximate the area of surfaces to the nearest square metre or square Centimetre.
Reasoning
Reasoning
Reasoning
102. Estimate and verify the area of shapes using square metres and centimetres, Reasoning and determine reasonableness of answer. 103. Develop and use formula to calculate the area of squares and rectangles. Reasoning 104. Draw different shapes of a given area on grids.
Reasoning
105. Calculate area of shapes drawn on a grid with unit squares.
Applying
106. Calculate the areas of compound shapes that may be dissected into rectangles and squares.
Applying
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Objective
Processes
107. Solve problems involving area and perimeter of plane shapes
Reasoning
108. Solve problems in real-life contexts involving area.
Reasoning
Volume and Capacity
109. State the relationship between the litre and millilitre and conve rt from one to the other. 110. Identify the cubic centimetre and cubic metre (cm³ and m³) as the standard units for measuring volume. 111. Measure the volume of boxes by stacking and packing cubic blocks into them and counting to determine the volume. 112. Calculate the volume of cubes and cuboids.
Knowing
113. State the relationship between the metric units of volume and capacity (e.g.1L = 1000 cm3). 114. Solve problems involving capacity, number and money.
Knowing
115. Solve problems involving volume/capacity.
Reasoning
Knowing Reasoning Applying
Reasoning
Mass
116. Measure and compare the masses/weights of objects in kilograms and grams using a set of scales. 117. Convert kilograms to grams and vice versa.
Knowing
118. State the relationship between the kilogram and gram
Knowing
119. Determine the most appropriate standard unit for measuring mass/weight.
Knowing
120. Calculate unknown mass/weight on a balance (including the use of algebraic reasoning). 121. Solve problems involving different units of mass/weight (e.g. Find the total mass/weight of three items weighing 50g, 750g and 2.5kg.
Reasoning
122. Solve computational and real-life problems involving grams and kilograms
Reasoning
123. Solve real-life problems involving mass/weight, number and money.
Reasoning
Knowing
Reasoning
Time
124. Tell time in five minute intervals using the digital and analog clocks.
Knowing
125. State the time after given intervals on analog and digital clocks.
Knowing
126. Match times shown on standard digital clocks, 24 hour digital clocks and analog clocks to the minute, and record the time.
Knowing
127. Calculate the duration of events using starting and finishing times (elapsed time). 128. Convert minutes to hours.
Applying
129. Convert hours to minutes.
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Knowing
Objective
Processes
130. Interpret simple time schedules (e.g. the calendar).
Knowing
131. Solve computational and real-life problems involving hours and minutes.
Reasoning
132. Solve problems involving time and other related concepts (using proportional reasoning).
Reasoning
Objectives and Thinking Processes for Geometry Strand Objective
Processes
Solids and Plane Shapes
133. Recognize solids from pictorial representations.
Knowing
134. Draw the faces of solids and explore their properties.
Applying
135. Describe the properties of solids in relation to number and types of faces, edges and vertices.
Knowing
136. Name the solids with uniform cross-sections.
Knowing
137. Solve problems involving solids.
Reasoning
138. Recognize plane shapes from pictorial representations.
Knowing
139. Investigate the properties of solids by examining their cross-sections, base, height and angles. 140. Solve problems involving plane shapes.
Applying
141. Construct and draw regular and irregular polygons given their properties using the principles of parallel and perpendicular lines, angles and number of sides. 142. Differentiate between regular and irregular polygons (triangles, quadrilaterals, pentagons, hexagons, octagons).
Applying
143. Describe the properties of specific quadrilaterals (rectangle, square, trapezium, parallelogram and rhombus) 144. Describe a given pattern (repeating, increasing or decreasing)
Knowing
145. Determine the pattern rule and extend the pattern using concrete materials or pictorial representation. 146. Classify and compare quadrilaterals according to their attributes (no. of sides and angles, no. of equal sides, no. of pairs of parallel sides, no. of perpendicular sides). 147. Classify triangles (same, similar or different) based on properties of sides and angles. 148. Identify and name triangles as scalene, right angled, isosceles and equilateral.
Applying
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Applying
Knowing
Applying
Applying
Applying Knowing
Objective
Processes
149. Compare and describe the properties of the sides and angles of the scalene, right angled, isosceles and equilateral triangles.
Applying
150. Create repeating, increasing and decreasing patterns using solids or plane shapes (concrete and pictorial) and explain the pattern rule.
Reasoning
151. Insert the missing elements in given patterns (concrete or pictorial) and explain the reasoning.
Reasoning
Symmetry
152. Determine whether plane shapes, letters and numerals are symmetrical.
Knowing
153. Complete a symmetrical shape given half of the shape and a line of symmetry. 154. Determine the number of lines of symmetry in plane shapes – (regular, irregular and curved) and in numerals and letters.
Applying
155. Create symmetrical shapes
Reasoning
156. Solve problems involving line symmetry.
Reasoning
Applying
Angles
157. Describe an amount of turn (e.g. whole turn, three quarter turn, half turn or quarter turn).
Applying
158. Recognize an angle as an amount of turn.
Knowing
159. Identify angles on faces of solids or plane shapes that are right angles, greater than right angles or smaller than right angles.
Knowing
160. Investigate angles (right angles, angles greater than and smaller than right angles) in regular and irregular polygons and faces of solids.
Applying
161. Describe an angle as a measure of turn and name the quarter turn as a right angle or the angle formed when perpendicular lines meet. 162. Draw shapes with angles of various sizes and describe the angles.
Knowing Reasoning
Objectives and Thinking Processes for Statistics Strand Objective
Processes
163. Represent data using tally charts, frequency tables and graphs (pictographs, block graphs, bar graphs) using various scale factor 164. Interpret the findings displayed in the tables, charts (including tally charts, no pie charts) and graphs (pictographs, block graphs, bar graphs).
Applying
165. Compare the effectiveness of different representations of the same data. 166. Determine a suitable scale for data and record the scale in a key.
Reasoning
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Reasoning
167. Use analysed data to solve problems, draw conclusions and make decisions. 168. Communicate findings and decisions made using appropriate vocabulary associated with statistics. 169. Determine the mode of a given set of data.
Reasoning
170. Apply findings from analysis of data to solve problems.
Applying
171. Evaluate decisions made based on analysis of data represented in tables, charts and graphs. 172. Calculate the mean of a given set of data.
Reasoning
173. Solve problems involving mean/average.
Reasoning
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Knowing
